The solution to the simplification of the algebraic expressions are;
A) 5p³q + 5pq³ + 5p²q
B) 14pqr² - 7p²qr
C) 20x² - 15xy - 16ax + 12ay
A) We have the expression;
5pq(p² + q² + pq)
Multiplying out using the concept of distributive property, we have;
(5pq × p²) + (5pq × q²) + (5pq × pq)
>> 5p³q + 5pq³ + 5p²q
B) We have the expression;
-7pr(pq – qr - rq)
Multiplying out using the concept of distributive property, we have;
-7p²qr + 7pqr² + 7pqr²
>> 14pqr² - 7p²qr
C) (4x - 3y)(5x - 4a)
By quadratic expansion, we have;
(4x * 5x) - (3y * 5x) - (4x * 4a) + (4a * 3y)
>> 20x² - 15xy - 16ax + 12ay
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A jaguar can run 40 miles per hour while a giraffe can run 32 per mile if they both run for 4 hours how much farther will the jaguar run? Show TWO ways to write the expression or equation and solve
Answer:
(40*4)-(32*4)=32
160-128=32
Step-by-step explanation:
A pet shop sells mice, rats and gerbils. The ratio of mice to rats is 4:3 and the ratio of mice to gerbils is 7:4. If there are 32 gerbils in stock at present, how many rats are there? Please could you explain your working out.
Answer:
42 rats.
Step-by-step explanation:
since the ratio of mice to gerbils is 7:4, given that there are 32 gerbils, that means 32/4=8 gerbils; in other words, 56mice:32gerbils. Then, to find the # of rats, the ratio is 4:3, so you take the previous value of the # of mice and divide it by 4 to get 14(3)= 42
To understand this question, we need to know what it's asking and what's important and what is not important. Many people skip this step, but it is very important.
It is asking us to Find how many Rats there are.
This problem is defiantly reduced to the simplistic ratio
The next step is to Find clues
The clues are 32 Gerbils, 7:4 and 4:3
Now i like to make a chart but you may skip this step if you want
Gerbils=32
Mice=??
Rats=??
First, we have to find the numbers of Mice.
(Reducing Ratios divide them by a number like 2:4=1:2)
If you have 32 Gerbils and you reduced it to 4, what did you dived?
32/4=8
So, you multiply 7x8=56
There is 56 Mice.
Our table looks like this
Gerbils=32
Mice=56
Rats=??
Now we use the ratio 4:3 to find the numbers of Rats
If there are 56 mice, and it is reduced to 4, we have to do 56/4 to find out what we have to multiply 3 by to get the total numbers of rats (Inverse Operation) by. We get 14.
So now we do 3x14 in which we get 42.
Our chart now looks like this
Gerbils=32
Mice=56
Rats=42
I Hope this helped if you have any questions just tell me
The students in Class A and Class B were asked how many pets they each have. The dot plots below show the
results
Students in Class A
Number of Pets
Students in Class B
What is the difference between the ranges in the dot plot
Answer:
The answer is 2
Step-by-step explanation:
The range of class A is 5-0 = 5
The range of class B is 3-0 = 3
the difference between 3 and 5 is 2.
Yesterday, Carmen went surfing and was out for 5 hours. Today, she spent 60% more time
than yesterday riding waves. How long was Carmen out surfing today?
Answer:
Today, Carmen out surfing for 8 hours
Step-by-step explanation:
160/100 × 5 = 8
The ratio of men to women working for a company is to 8 to 5 . If there are employees total 208 , how many women work for the company?
Answer:
130
ratio of woman to man is : 5/8
5/8×208=130
Answer:
130 women
Step-by-step explanation:
3 men to 5 women:
We can add the variable x:
3x + 5x = 208
8x = 208
x = 26
3 * 26 = 78 men,
5 * 26 = 130 women.
el valor númerico del término n=15 de la sucesión 5 20 80... es?
Answer:
É 5x3=15
Step-by-step explanation:
Help me with this question lol
Answer:
i think that it would be 0
Please help me with this
Answer:
The measure of <Y = 85 degrees
Step-by-step explanation:
you can solve this problem algebraically if you know that the sum of the interior angles of a triangle is 180 degrees.
if you add all of these angles and set them equal to 180, you can find what "a" is.
a+2a+a+10=180 so 4a+10=180 so a is 42.5 (which is equal to angle x)
then looking at all of the options, it can be seen that the first two options are incorrect because angle x is equal to 42.5 degrees.
you know that angle y is equal to 2a, so multiplying "a" by two, you can find that angle y is 85 degrees.
sin(83)cos(7) + cos(83)sin(7)
Answer:
1
Step-by-step explanation:
correct on edge
sin(83 radians) * cos(7 radians)) + (cos(83 radians) * sin(7 radians)) =
0.893996664
Answer:
hope it helps
At the end of the year, company A paid a dividend of 3,000 VND/share. Speed
constant annual dividend growth of 5%.
The current selling price of stock A is VND 60,000/share.
Definition of cost of common equity
Answer:
all u do is take 3000×5%=150
PLEASE help me answer this!!!
Check the picture below.
Which equation correctly uses the law of cosines to solve for y? 92 = y2 + 192 – 2(y)(19)cos(41°) y2 = 92 + 192 – 2(y)(19)cos(41°) 92 = y2 + 192 – 2(9)(19)cos(41°) y2 = 92 + 192 – 2(9)(19)cos(41°) PLS HELP!!
Answer:
[tex]Fourth \: option: y^2=9^2+19^2-2(9)(19) cos(41°)[/tex]
[tex]The \: law \: of \: cosines \: to \: solve \: for \: one \: side \: is:[/tex]
[tex]c^2=a^2+b^2-2ab \: cos \: C[/tex]
We must know the other two sides (a and b) and the angle between these sides (angle C, the opposite to the side that we want to determine)
In this case c=y, a=9, b=19, and C=41°, then:
[tex]y^2=9^2+19^2-2(9)(19) \: cos \: (41°)[/tex]
An ice cream stand uses the expression to determine the cost (in dollars) of an ice cream cone that has scoops of ice cream.2 + 0.5x2+0. 5x2, plus, 0, dot, 5, xxxx
How much does an ice cream cone with scoops cost?55
Answer:
answer: 0
Step-by-step explanation:
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
(x+4)•(x-1)
——————————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
(x+4) • (x-1) = 0
7.2 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
simple form
x = 1
x = -4
Find the area for each of the given shapes below. If a shape has shading, find the area of the shaded region only.
Answer:
a. 39 ft²
c. 2x² +11x +12
e. 35 yd²
Step-by-step explanation:
a.The missing vertical dimension is 5-3 = 2'. The missing horizontal dimension is 11-8 = 3'. Then the figure can be decomposed into a rectangle 11'×3' and one that is 3'×2'. The sum of those areas is ...
total area = (11 ft)(3 ft) +(3 ft)(2 f) = (3 ft)(11 +2 ft) = (3 ft)(13 ft) = 39 ft²
__
c.We don't know what to make of the rectangles in each corner, so we'll assume they are distorted right-angle indicators. The area is the product of the dimensions shown:
A = LW
A = (2x +3)(x +4) = 2x² +11x +12 . . . area of figure
__
e.The shaded area is half the area of the rectangle. That is the same area you get if you use the triangle formula for the area of the shaded triangle.
A = 1/2(14 yd)(5 yd) = 35 yd²
3x2 - 4x – 7
factor
Answer:
3x2 = 6
6-4x-7
(6-4x) - 7
2x - 7 = messi ok no xd
3.5-
Step-by-step explanation:
Answer:
[tex](3x-7)(x+1)[/tex]
Step-by-step explanation:
Use the slide-and-divide method:
[tex]3x^2-4x-7[/tex]
[tex]x^2-4x-21[/tex] <-- Multiply last term by the leading coefficient 3
[tex](x-7)(x+3)[/tex] <-- Factor
[tex](3x-7)(x+1)[/tex]
Find the quotient: 7,308 divided by 18. A) 46 B) 406 C) 406 10/18. D) 408
Answer:
7308 / 18
= 406
B is the answer.
Simplify 1.25 (-x -4)
Answer:
1.25(-xsquare - 8x + 16)
Step-by-step explanation:
pls give me brainliest
I'm not sure but I think so
90 is 95% of what number?
Answer:
94.74
Step-by-step explanation:
Hope this helps!
Answer:
94.74
Step-by-step explanation:
Help anyone?? Not that hardd
no links ! :(
Answer:
1.2
Step-by-step explanation:
First, you cancel out [tex]\frac{6}{20}[/tex] to become [tex]\frac{3}{10}[/tex]
Then that becomes [tex]-\frac{3}{10}+1.5[/tex]
Now, you convert the element to a decimal form to be [tex]-0.3+1.5[/tex]
Finally, you subtract them (because a negative plus a positive is subtraction) to get the final answer of 1.2
Hope this helps!
1) A museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Let x represent the amount borrowed at 7%, y represent the amount borrowed at 8.5%, and z represent the amount borrowed at 9.5%. Set up a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. Then write the system in matrix form. You do not have to solve the system.
Based on the information the amount borrowed at each rate is:
Z=9.5%=$350,000Y= 8.5%=$1,400,000X=7% =$250,000Let x=9.5%
Let 4x= 8.5%
Let 7% =$2,000,000 - 5x
Formulate
0.095x + 0.085(4x) + 0.07(2,000,000-5x) = 169,750
Collect like terms
0.095x + 0.34x + 140,000 - 0.35x = 169,750
Divide both side by 0.085x
0.085x = 29,750
x=29,750/0.085
x =$350,000
Amount borrowed at each rate:
Z=9.5% =$350,000
Y= 8.5% =$350,000×4
Y= 8.5% =$1,400,000
X=7% =$2,000,000 - 5($350,000)
X=7%=$2,000,000-$1,750,000
X=7% =$250,000
Matrix form
Z $350,000
Y $1,400,000
X $250,000
Inconclusion the amount borrowed at each rate is: $350,000; $1,400,000; $250,000.
Learn more about amount borrowed here:https://brainly.com/question/24576997
I need help with 7c please
Answer:
mx x 2 x1dadqd
Step-by-step explanation:
Josh and Adelina are staff members for a political candidate. They are considering hiring callers who will call voters and ask for donations. (picture below)
a) only adelina's
b) only josh's
c) both statements are correct
d) neither statements are correct
Answer:
Adelina
Step-by-step explanation:
Which of the following are steps in practical problem solving?
Answer:
Assign an identifying variable to the quantity to be found. Write a sentence stating conditions placed on the quantity. Solve the sentence for the variable.
Step-by-step explanation:
can you mark me as brainlist
Roy used 1/4 of his money on 3 pens and 6 notebooks. The cost of each pen is 3 times the cost of each notebook. He bought some more pens with 2/3 of his remaining money. How many pens did Roy buy altogether?
=========================================================
Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
---------------
In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
---------------
In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
--------------
Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
Help me plzzzzzzz! I need this today!
Answer:
it looks like y int is about 2550
Step-by-step explanation:
Wite a numerical expression for the below problems. Simplify the expressions.
Multiply six times three then divide by lwo
The quotient of twelve and two subiracled from thirty-six
Answer:
1) 9
2) 34
Step-by-step explanation:
For the first one, it would be
= (6×3)/2
= 18/2
= 9
The second one is,
= 36- (12/6)
= 36 - 2
= 34
he school that Tony goes to is selling tickets to a play. On the first day of ticket sales the school
sold 9 adult tickets and 8 student tickets for a total of $164. The school took in $73 on the second
day by selling 2 adult tickets and 7 student tickets.
What is the price each of one adult ticket?
What is the price each of one student ticket?
Plz explain how to do this
Answer:
The price of 1 adult ticket is 12 dollars, and the price of a ticket for one student is 7 dollars
Step-by-step explanation:
Make a system of equations for the two days that the play was shown.
Let x = the price of an adult ticket
Let y = the price of a student ticket
For the first day:
9x+8y=164For the second day:
2x+7y=73Now, we can solve using the elimination method. Multiply the first equation by 2 and the second equation by 9. Then swap the order of the equations.
18x+63y= 657-18x+16y= 3280x+ 47y= 329divide both sides by 47y = 7Plug in 7 for y for the 2nd equation2x+7(7)=732x+49=73subtract 49 from both sides2x= 24divide both sides by 2x = 12 Check:2(12)+7(7)=7324+49= 73!Answer: And I don’t know math
Step-by-step explanation:
which expression is equivalent to (tan(θ/2))(sin θ)
Answer:
B) [tex]-1+cos\theta[/tex]
Step-by-step explanation:
[tex](tan(\frac{\theta}{2}))(-sin\theta)[/tex]
[tex](\frac{1-cos\theta}{sin\theta})(-sin\theta)[/tex]
[tex](\frac{-sin\theta+sin\theta cos\theta}{sin\theta})[/tex]
[tex]-1+cos\theta[/tex]
Therefore, option B is correct
Helpful Tips:
Half-Angle Formula: [tex]tan(\frac{\theta}{2})= \frac{1-cos\theta}{sin\theta}=\frac{sin\theta}{1+cos\theta}=\pm\sqrt{\frac{1+cos\theta}{2}}[/tex]
A U.S. citizen invested a $1200 government stimulus check they received on March 1, 2020,
into stocks that grew with an annual percentage rate of 20.2%, compounded continuously.
How much are these stocks worth 9 months later on December 1, 2020? Round to two
decimal place accuracy. (Hint: 9 months = 0.75 years)
The stocks are worth $ 1396.29 nine months later.
Using the continuous compounding formula,
[tex]A = Pe^{rt}[/tex] where
A = final amount of stocks P = initial amount of stocks = $1200, r = compounding rate = 20.2 % = 0.202 t = 9 months = 0.75 yearsSubstituting the values of the variables into the equation, we have
[tex]A = Pe^{rt}[/tex]
[tex]A = 1200e^{0.202 X 0.75}\\A = 1200e^{0.1515}\\A = 1200(1.1636)\\A = 1396.29[/tex]
So, the stocks are worth $ 1396.29 nine months later.
Learn more about continuous compounding here:
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Dave and Kyle are 40 miles apart on a path when they start moving toward each other. Dave runs at a constant speed of 8 miles per hour, while Kyle walks at a constant speed of 5 miles per hour. How long does it take until they meet?
Answer:
About 3 hours
Step-by-step explanation:
together, they go 13 miles in one hour. 40/13 = 3 with remainder 1